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Decide whether or not the function is continuous. If it is not continuous, identify the points at which it is discontinuous.$$f(x)=x^{2}+\frac{1}{x}$$

Non-rem. disc. At $x=0$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 3

Limits and Continuity

Derivatives

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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in this problem, we have to decide whether or not the function is continuous. If it is not continuous identify, we have to identify the points at which it is discontinuous, so the given function is F of X is equal to extra pair. Bless what up on X For a function to be continuous, it should be defined for it should be defined everywhere. So if we plug if we plug X is equal to zero in f of X in f of X, we have an undefined form. We have an undefined form. We know that went up on zero is an intermediate form, so we cannot find the value of the function at X is equal to zero. So we can say that this function is not defined at X is equal to zero. Or we can say that this function is discontinuous. Discontinuous at X is equal to zero except X is equal to zero. This from the given function is continuous everywhere except X is equal to zero

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